A simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 103 , and the sample standard deviation, s , is found to be 12 . (a) Construct a \( 95 \% \) confidence interval about \( \mu \) if the sample size, \( n \), is 20 . (b) Construct a \( 95 \% \) confidence interval about \( \mu \) if the sample size, \( n \), is 14. (c) Construct a \( 90 \% \) confidence interval about \( \mu \) if the sample size, \( n \), is 20 . (d) Should the confidence intervals in parts (a)-(c) have been computed if the population had not been normally distributed? Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? B. As the level of confidence decreases, the size of the interval decreases. B. As the level of confidence decreases, the size of the interval stays the same.

The probability of committing a Type I error: is solely determined by the size of the treatment effect. cannot be controlled by the experimenter. is determined by the alpha (a) level that one chooses. is determined by the beta ( \( \beta \) ) level one chooses. is determined by the sample size that one chooses.

A researcher risks a Type I error: anytime HO is rejected. anytime H 1 is rejected. anytime HO is accepted. anytime the sample size is increased.

The estimated standard error (SM), provides a measure of the average discrepancy between: a score ( x ) and the population mean ( \( \mu \) ). a sample mean (M) and the population mean ( \( \mu \) ). the sample standard deviation ( s ) and the population standard deviation ( \( (\mathrm{O} \) ).

The null hypothesis: predicts that the treatment will have no effect. predicts that the treatment will have an effect. is denoted by the symbol H1. is always stated in terms of sample statistics.

If we say that we have statistically significant results, we mean that the results are: very important. meaningless. likely to be due to chance differences between to be due to true differences between the groups.